Problem: Simplify the following expression: $a = \dfrac{z^2 + 6z - 16}{z + 8} $
Explanation: First factor the polynomial in the numerator. $ z^2 + 6z - 16 = (z + 8)(z - 2) $ So we can rewrite the expression as: $a = \dfrac{(z + 8)(z - 2)}{z + 8} $ We can divide the numerator and denominator by $(z + 8)$ on condition that $z \neq -8$ Therefore $a = z - 2; z \neq -8$